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Throughout the long history of the nonlinear Schrödinger equation (NLSE), many exact analytical solutions have been found and they continue to grow as new solutions are being sought and discovered. This book aims to organize the solutions by classifying and grouping them based on aspects and symmetries they possess. The authors present a systematic derivation of many solutions and even include new derivations. This expanded second edition contains new solutions published or derived since the first edition. Noting the increasing interest in and applications of the fractional nonlinear Schrödinger equation, a new chapter devoted to this topic has been added. Each chapter now also features an introductory section documenting the history, background, and physical systems described by the equations at hand.
Key Features:
- Comprehensive and fully up to date, with detailed consideration of the main NLSE models.
- Includes animated figures to help visualize solutions and their dynamics.
- Accompanied by Mathematica codes, including dynamics of solutions.
- New chapter on the Fractional Nonlinear Schrödinger Equation.
Preface to first edition
Preface to second edition
Notation
Acknowledgements
Author biographies
1 Introduction
2 Fundamental nonlinear Schrödinger equation
3 Nonlinear Schrödinger equation with power law and dual power law nonlinearities
4 Nonlinear Schrödinger equation with higher order terms
5 Scaling transformations
6 Nonlinear Schrödinger equation in (N + 1)-dimensions
7 Coupled nonlinear Schrödinger equations
8 Discrete nonlinear Schrödinger equation
9 Nonlocal nonlinear Schrödinger equation
10 Fractional nonlinear Schrödinger equation
Appendix A: Derivation of some solutions of chapters 2 and 3
Appendix B: Darboux transformation: single soliton and breather solutions
Appendix C: Derivation of the similarity transformations in chapter 5